Unscented guidance

Abstract

Unscented guidance combines the concept of the unscented transform with standard optimal control theory to produce an open-loop method to manage uncertainties in nonlinear dynamical systems. The theoretical foundations for this concept can be framed in terms of a low-order semi-discretization of a Lebesgue-Stieltjes optimal control problem. A Zermelo problem subject to parameter uncertainties is used to quantitatively demonstrate the substantial reductions in target error statistics (95% in mean and 70% in the trace of the covariance) through the use of unscented guidance. These ideas generate a tractable approach for solving chance-constrained optimal control problems.